COMPOSITION ALGEBRAS WITH LARGE DERIVATION ALGEBRAS

The finite dimensional flexible composition algebras include the Hurwi tz algebras (composition algebras with unit element), but also other i nteresting classes of algebras: the para-Hurwitz and the Okubo algebra s. The above mentioned algebras present many symmetries, and this is r eflected in their large derivation algebras. In the present paper we s tudy the opposite question: What can be said about the composition alg ebras if we have some information about their derivation algebras? Our main result is the classification of all the composition algebras wit h such large derivation algebras. (C) 1997 Academic Press.